{ "metadata": { "name": "Priors" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#Chapter 6\n", "\n", "This chapter of [Bayesian Methods for Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers) focuses on the most debated and discussed part of Bayesian methodologies: how to choose an appropriate prior distribution. We also present how the prior's influence changes as our dataset increases, and an interesting relationship between priors and penalties on linear regression.\n", "\n", "## Getting our priorities straight\n", "\n", "\n", "Up until now, we have mostly ignored our choice of priors. This is unfortunate as we can be very expressive with our priors, but we also must be careful about choosing them. This is especially true if we want to be objective, that is, not express any personal beliefs in the priors. \n", "\n", "###Subjective vs Objective priors\n", "\n", "Bayesian priors can be classified into two classes: *objective* priors, which aim to allow the data to influence the posterior the most, and *subjective* priors, which allow the practitioner to express his or her views into the prior. \n", "\n", "What is an example of a objective prior? We have seen some already, including the *flat* prior (which is a uniform distribution over the entire possible range of the unknown). Using a flat prior implies we give each possible value an equal weighting. Choosing this type of prior is invoking what is called \"The Principle of Indifference\", literally we have no a prior reason to favor one value over another. Though similar, but not correct, is calling a flat prior over a restricted space an objective prior. For example, if we know $p$ in a Binomial model is greater than 0.5, then $\\text{Uniform}(0.5,1)$ is not an objective prior (since we have used prior knowledge) even though it is \"flat\" over [0.5, 1]. The flat prior must be flat along the *entire* range of possibilities. \n", "\n", "Aside from the flat prior, other examples of objective priors are less obvious, but they contain important characteristics that reflect objectivity. For now, it should be said that *rarely* is a objective prior *truly* objective. We will see this later. \n", "\n", "#### Subjective Priors\n", "\n", "On the other hand, if we added more probability mass to certain areas of the prior, and less elsewhere, we are biasing our inference towards the unknowns existing in the former area. This is known as a subjective, or *informative* prior. In the figure below, the subjective prior reflects a belief that the unknown likely lives around 0.5, and not around the extremes. The objective priors is insensitive to this." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "\n", "import scipy.stats as stats\n", "figsize(12.5,3)\n", "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", "\n", "x = np.linspace(0,1)\n", "y1, y2 = stats.beta.pdf(x, 1,1), stats.beta.pdf(x, 10,10)\n", "\n", "p = plt.plot( x, y1, \n", " label='An objective prior \\n(uninformative, \\n\"Principle of Indifference\" )' )\n", "plt.fill_between( x, 0, y1, color = p[0].get_color(), alpha = 0.3 )\n", "\n", "p = plt.plot( x,y2 ,\n", " label = \"A subjective prior \\n(informative)\" )\n", "plt.fill_between( x, 0, y2, color = p[0].get_color(), alpha = 0.3 )\n", "\n", "p = plt.plot( x[25:], 2*np.ones(25), label = \"another subjective prior\" )\n", "plt.fill_between( x[25:], 0, 2, color = p[0].get_color(), alpha = 0.3 )\n", "\n", "plt.ylim(0,4)\n", "\n", "plt.ylim(0, 4)\n", "leg = plt.legend(loc = \"upper left\")\n", "leg.get_frame().set_alpha(0.4)\n", "plt.title(\"Comparing objective vs. subjective priors for an unknown probability\" );" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", "For more information, type 'help(pylab)'.\n" ] }, { "output_type": "display_data", "png": 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bSWylpaUS3Z+iKIqiKEoSaBJeB39/f9jb22PcuHHw9/cX2ubp6YnFixfDxcUF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\nRBVVta5qK4Hs7GzzbPSNpDcnJ4erV69y9OhRGjd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NmowbN87SoVillJQUevfuzdatW7G1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\nGpj8/ARzA43iuu8kPD09Ha1Wi6OjIxs2bOC5557j5MmC/VA3b95MixY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} ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The choice of a subjective prior does not always imply that we are using the practitioner's subjective opinion: more often the subjective prior was once a posterior to a previous problem, and now the practitioner is updating this posterior with new data. A subjective prior can also be used to inject *domain knowledge* of the problem into the model. We will see examples of these two situations later." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Decision, decisions...\n", "\n", "The choice, either *objective* or *subjective* mostly depend on the problem being solved, but there are a few cases where one is preferred over the other. In instances of scientific research, the choice of an objective prior is obvious. This eliminates any biases in the results, and two researchers who might have differing prior opinions would feel an objective prior is fair. Consider a more extreme situation:\n", "\n", "> A tobacco company publishes an report with a Bayesian methodology that retreated 60 years of medical research on tobacco use. Would you believe the results? Unlikely. The researchers probably choose a subjective prior that too strongly biased results in their favor.\n", "\n", "Unfortunately, choosing an objective prior is not as simple as selecting a flat prior, and even today the problem is still not completely solved. The problem with naively choosing the uniform prior is that pathological issues can arise. Some of these issues are pedantic, but we delay more serious issues to the Appendix of this Chapter (TODO)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We must remember that choosing a prior, whether subjective or objective, is still part of the modeling process. To quote Gelman [5]:\n", "\n", ">...after the model has been \ufb01t, one should look at the posterior distribution\n", "and see if it makes sense. If the posterior distribution does not make sense, this implies\n", "that additional prior knowledge is available that has not been included in the model,\n", "and that contradicts the assumptions of the prior distribution that has been used. It is\n", "then appropriate to go back and alter the prior distribution to be more consistent with\n", "this external knowledge.\n", "\n", "If the posterior does not make sense, then clearly one had an idea what the posterior *should* look like (not what one *hopes* it looks like), implying that the current prior does not contain all the prior information and should be updated. At this point, we can discard the current prior and choose a more reflective one.\n", "\n", "Gelman [4] suggests that using a uniform distribution, with a large bounds, is often a good choice for objective priors. Although, one should be wary about using Uniform objective priors with large bounds, as they can assign too large of a prior probability to non-intuitive points. Ask: do you really think the unknown could be incredibly large? Often quantities are naturally biased towards 0. A Normal random variable with large variance (small precision) might be a better choice, or an Exponential with a fat tail in the strictly positive (or negative) case. \n", "\n", "If using a particularly subjective prior, it is your responsibility to be able to explain the choice of that prior, else you are no better than the tobacco company's guilty parties. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Empirical Bayes\n", "\n", "While not a true Bayesian method, *empirical Bayes* is a trick that combines frequentist and Bayesian inference. As mentioned previously, for (almost) every inference problem there is a Bayesian method and a frequentist method. The significant difference between the two is that Bayesian methods have a prior distribution, with hyperparameters $\\alpha$, while empirical methods do not have any notion of a prior. Empirical Bayes combines the two methods by using frequentist methods to select $\\alpha$, and then proceeding with Bayesian methods on the original problem. \n", "\n", "A very simple example follows: suppose we wish to estimate the parameter $\\mu$ of a Normal distribution, with $\\sigma = 5$. Since $\\mu$ could range over the whole real line, we can use a Normal distribution as a prior for $\\mu$. How to select the prior's hyperparameters, denoted ($\\mu_p, \\sigma_p^2$)? The $\\sigma_p^2$ parameter can be chosen to reflect the uncertainty we have. For $\\mu_p$, we have two options:\n", "\n", "1. Empirical Bayes suggests using the empirical sample mean, which will center the prior around the observed empirical mean:\n", "\n", "$$ \\mu_p = \\frac{1}{N} \\sum_{i=0}^N X_i $$\n", "\n", "2. Traditional Bayesian inference suggests using prior knowledge, or a more objective prior (zero mean and fat standard deviation).\n", "\n", "Empirical Bayes can be argued as being semi-objective, since while the choice of prior model is ours (hence subjective), the parameters are solely determined by the data.\n", "\n", "Personally, I feel that Empirical Bayes is *double-counting* the data. That is, we are using the data twice: once in the prior, which will influence our results towards the observed data, and again in the inferential engine of MCMC. This double-counting will understate our true uncertainty. To minimize this double-counting, I would only suggest using Empirical Bayes when you have *lots* of observations, else the prior will have too strong of an influence. I would also recommend, if possible, to maintain high uncertainty (either by setting a large $\\sigma_p^2$ or equivalent.)\n", "\n", "Empirical Bayes also violates a theoretical axiom in Bayesian inference. The textbook Bayesian algorithm of:\n", "\n", ">*prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior* \n", "\n", "is violated by Empirical Bayes, which instead uses \n", "\n", ">*observed data* $\\Rightarrow$ *prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior*\n", "\n", "Ideally, all prior should be specified *before* we observe the data, so that the data does not influence our prior opinions (see the volumes of research by Daniel Kahnem *et. al* about [anchoring](http://en.wikipedia.org/wiki/Anchoring_and_adjustment) )." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Useful priors to know about\n", "\n", "### The Gamma distribution\n", "\n", "A Gamma random variable, denoted $X \\sim \\text{Gamma}(\\alpha, \\beta)$, is a random variable over the positive real numbers. It is in fact a generalization of the Exponential random variable, that is:\n", "\n", "$$ \\text{Exp}(\\beta) \\sim \\text{Gamma}(1, \\beta) $$\n", "\n", "This additional parameter allows the probability density function to have more flexibility, hence allows the practitioner to express his or her subjective priors more accurately. The density function for a $\\text{Gamma}(\\alpha, \\beta)$ random variable is:\n", "\n", "$$ f(x \\mid \\alpha, \\beta) = \\frac{\\beta^{\\alpha}x^{\\alpha-1}e^{-\\beta x}}{\\Gamma(\\alpha)} $$\n", "\n", "where $\\Gamma(\\alpha)$ is the [Gamma function](http://en.wikipedia.org/wiki/Gamma_function), and for differing values of $(\\alpha, \\beta)$ looks like:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.5, 5 )\n", "gamma = stats.gamma\n", "\n", "parameters = [ (1, 0.5), (9, 2), (3, 0.5 ), (7, 0.5) ]\n", "\n", "\n", "x = linspace( 0.001 ,20, 150 )\n", "for alpha, beta in parameters:\n", " y = gamma.pdf(x, alpha, scale=1./beta)\n", " lines = plt.plot( x, y, label = \"(%.1f,%.1f)\"%(alpha,beta), lw = 3 )\n", " plt.fill_between( x, 0, y, alpha = 0.2, color = lines[0].get_color() )\n", " plt.autoscale(tight=True)\n", " \n", "plt.legend(title=r\"$\\alpha, \\beta$ - parameters\")" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", 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EvCVHIfsCfIBWjXAfyzI2JjPwfR4fxiQiIiIi+yX7AhwAJrANhfoI16QluWLu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\n62it6aK1Zj1hb8OSi+2pcPs0mjo1mjodFzazaJMYNUmMOoI8MWZiTwo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} ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Wishart distribution\n", "\n", "Until now, we have only seen random variables that a scalars. Of course, we can also have *random matrices*! Specifically, the Wishart distribution is a distribution over all [positive semi-definite matrices](http://en.wikipedia.org/wiki/Positive-definite_matrix). Why is this useful to have in our arsenal? (Proper) covariance matrices are positive-definite, hence the Wishart is an appropriate prior for covariance matrices. We can't really visualize a distribution of matrices, so I'll plot some realizations from the $5 \\times 5$ (above) and $20 \\times 20$ (below) Wishart distribution:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pymc as mc\n", "\n", "n = 4\n", "for i in range( 10 ):\n", " ax = plt.subplot( 2, 5, i+1)\n", " if i >= 5:\n", " n = 15\n", " plt.imshow( mc.rwishart( n+1, np.eye(n) ), interpolation=\"none\", \n", " cmap = plt.cm.hot ) \n", " \n", " ax.axis(\"off\")\n", "plt.suptitle(\"Random matrices from a Wishart Distribution\" );" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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} ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "One thing to notice is that the symmetry of these matrices. The Wishart distribution can be a little troubling to deal with, but we will use it in an example later." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Beta distribution\n", "\n", "You may have seen the term `beta` in previous code in this book. Often, I was implementing a Beta distribution. The Beta distribution is very useful in Bayesian statistics. A random variable $X$ has a $\\text{Beta}$ distribution, with parameters $(\\alpha, \\beta)$, if its density function is:\n", "\n", "$$f_X(x | \\; \\alpha, \\beta ) = \\frac{ x^{(\\alpha - 1)}(1-x)^{ (\\beta - 1) } }{B(\\alpha, \\beta) }$$\n", "\n", "where $B$ is the [Beta function](http://en.wikipedia.org/wiki/Beta_function) (hence the name). The random variable $X$ is only allowed in [0,1], making the Beta distribution a popular distribution for decimal values, probabilities and proportions. The values of $\\alpha$ and $\\beta$, both positive values, provide great flexibility in the shape of the distribution. Below we plot some distributions:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.5, 5 )\n", "import scipy.stats as stats\n", "\n", "params = [ (2,5), (1,1), (0.5, 0.5), ( 5, 5), (20, 4), (5, 1)]\n", "\n", "x = np.linspace( 0.01, .99, 100 )\n", "beta = stats.beta\n", "for a, b in params:\n", " y = beta.pdf( x, a, b )\n", " lines = plt.plot( x, y, label = \"(%.1f,%.1f)\"%(a,b), lw = 3 )\n", " plt.fill_between( x, 0, y, alpha = 0.2, color = lines[0].get_color() )\n", " plt.autoscale(tight=True)\n", "plt.ylim(0)\n", "plt.legend(loc = 'upper left', title=\"(a,b)-parameters\");" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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P14qVg7qYiRgV55d7SRIt/ErWbRXekLgR3pC4Ed6qHTuV2X9SXwcPn4JGqwvE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\nNXuBU30vcyX9bmmr1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} ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "One thing I'd like the reader to notice is the presence of the flat distribution above, specified by parameters $(1,1)$. This is the Uniform distribution. Hence the Beta distribution is a generalization of the Uniform distribution, something we will revisit many times.\n", "\n", "There is an interesting connection between the Beta distribution and the Binomial distribution. Suppose we are interested in some unknown proportion or probability $p$. We assign a $\\text{Beta}(\\alpha, \\beta)$ prior to $p$. We observe some data generated by a Binomial process, say $X \\sim \\text{Binomial}(N, p)$, with $p$ still unknown. Then our posterior *is again a Beta distribution*, i.e. $p | X \\sim \\text{Beta}( \\alpha + X, \\beta + N -X )$. Succinctly, one can relate the two by \"a Beta prior with Binomial observations creates a Beta posterior\". This is a very useful property, both computationally and heuristically.\n", "\n", "In light of the above two paragraphs, if we start with a $\\text{Beta}(1,1)$ prior on $p$ (which is a Uniform), observe data $X \\sim \\text{Binomial}(N, p)$, then our posterior is $\\text{Beta}(1 + X, 1 + N - X)$. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#####Example: Bayesian Multi-Armed Bandits\n", "*Adapted from an example by Ted Dunning of MapR Technologies*\n", "\n", "> Suppose you are faced with $N$ slot machines (colourfully called multi-armed bandits). Each bandit has an unknown probability of distributing a prize (assume for now the prizes are the same for each bandit, only the probabilities differ). Some bandits are very generous, others not so much. Of course, you don't know what these probabilities are. By only choosing one bandit per round, our task is devise a strategy to maximize our winnings.\n", "\n", "Of course, if we knew the bandit with the largest probability, then always picking this bandit would yield the maximum winnings. So our task can be phrased as \"Find the best bandit, and as quickly as possible\". \n", "\n", "The task is complicated by the stochastic nature of the bandits. A suboptimal bandit can return many winnings, purely by chance, which would make us believe that it is a very profitable bandit. Similarly, the best bandit can return many duds. Should we keep trying losers then, or give up? \n", "\n", "A more troublesome problem is, if we have a found a bandit that returns *pretty good* results, do we keep drawing from it to maintain our *pretty good score*, or do we try other bandits in hopes of finding an *even-better* bandit? This is the exploration vs. exploitation dilemma.\n", "\n", "### Applications\n", "\n", "\n", "The Multi-Armed Bandit problem at first seems very artificial, something only a mathematician would love, but that is only before we address some applications:\n", "\n", "- Internet display advertising: companies have a suite of potential ads they can display to visitors, but the company is not sure which ad strategy to follow to maximize sales. This is similar to A/B testing, but has the added advantage of naturally minimizing strategies that do not work (and generalizes to A/B/C/D... strategies)\n", "- Ecology: animals have a finite amount of energy to expend, and following certain behaviours has uncertain rewards. How does the animal maximize its fitness?\n", "- Finance: which stock option gives the highest return, under time-varying return profiles.\n", "- Clinical trials: a researcher would like to find the best treatment, out of many possible treatment, while minimizing losses. \n", "- Psychology: how does punishment and reward effect our behaviour? How do humans' learn?\n", "\n", "Many of these questions above a fundamental to the application's field.\n", "\n", "It turns out the *optimal solution* is incredibly difficult, and it took decades for an overall solution to develop. There are also many approximately-optimal solutions which are quite good. The one I wish to discuss is one of the few solutions that can scale incredibly well. The solution is known as *Bayesian Bandits*.\n", "\n", "\n", "### A Proposed Solution\n", "\n", "\n", "Any proposed strategy is called an *online algorithm* (not in the internet sense, but in the continuously-being-updated sense), and more specifically a reinforcement learning algorithm. The algorithm starts in an ignorant state, where it knows nothing, and begins to acquire data by testing the system. As it acquires data and results, it learns what the best and worst behaviours are (in this case, it learns which bandit is the best). With this in mind, perhaps we can add an additional application of the Multi-Armed Bandit problem:\n", "\n", "- Psychology: how does punishment and reward effect our behaviour? How do humans' learn?\n", "\n", "\n", "The Bayesian solution begins by assuming priors on the probability of winning for each bandit. In our vignette we assumed complete ignorance of the these probabilities. So a very natural prior is the flat prior over 0 to 1. The algorithm proceeds as follows:\n", "\n", "For each round:\n", "\n", "1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", "2. Select the bandit with largest sample, i.e. select $B = \\text{argmax}\\;\\; X_b$.\n", "3. Observe the result of pulling bandit $B$, and update your prior on bandit $B$.\n", "4. Return to 1.\n", "\n", "That's it. Computationally, the algorithm involves sampling from $N$ distributions. Since the initial priors are $\\text{Beta}(\\alpha=1,\\beta=1)$ (a uniform distribution), and the observed result $X$ (a win or loss, encoded 1 and 0 respectfully) is Binomial, the posterior is a $\\text{Beta}(\\alpha=1+X,\\beta=1+1\u2212X)$.\n", "\n", "To answer our question from before, this algorithm suggests that we should not discard losers, but we should pick them at a decreasing rate as we gather confidence that there exist *better* bandits. This follows because there is always a non-zero chance that a loser will achieve the status of $B$, but the probability of this event decreases as we play more rounds (see figure below).\n", "\n", "Below we implement Bayesian Bandits using two classes, `Bandits` that defines the slot machines, and `BayesianStrategy` which implements the above learning strategy." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pymc import rbeta\n", "\n", "rand = np.random.rand\n", "\n", "class Bandits(object):\n", " \"\"\"\n", " This class represents N bandits machines.\n", "\n", " parameters:\n", " p_array: a (n,) Numpy array of probabilities >0, <1.\n", "\n", " methods:\n", " pull( i ): return the results, 0 or 1, of pulling \n", " the ith bandit.\n", " \"\"\"\n", " def __init__(self, p_array):\n", " self.p = p_array\n", " self.optimal = np.argmax(p_array)\n", " \n", " def pull( self, i ):\n", " #i is which arm to pull\n", " return rand() < self.p[i]\n", " \n", " def __len__(self):\n", " return len(self.p)\n", "\n", " \n", "class BayesianStrategy( object ):\n", " \"\"\"\n", " Implements a online, learning strategy to solve\n", " the Multi-Armed Bandit problem.\n", " \n", " parameters:\n", " bandits: a Bandit class with .pull method\n", " \n", " methods:\n", " sample_bandits(n): sample and train on n pulls.\n", "\n", " attributes:\n", " N: the cumulative number of samples\n", " choices: the historical choices as a (N,) array\n", " bb_score: the historical score as a (N,) array\n", " \"\"\"\n", " \n", " def __init__(self, bandits):\n", " \n", " self.bandits = bandits\n", " n_bandits = len( self.bandits )\n", " self.wins = np.zeros( n_bandits )\n", " self.trials = np.zeros(n_bandits )\n", " self.N = 0\n", " self.choices = []\n", " self.bb_score = []\n", "\n", " \n", " def sample_bandits( self, n=1 ):\n", " \n", " bb_score = np.zeros( n )\n", " choices = np.zeros( n )\n", " \n", " for k in range(n):\n", " #sample from the bandits's priors, and select the largest sample\n", " choice = np.argmax( rbeta( 1 + self.wins, 1 + self.trials - self.wins) )\n", " \n", " #sample the chosen bandit\n", " result = self.bandits.pull( choice )\n", " \n", " #update priors and score\n", " self.wins[ choice ] += result\n", " self.trials[ choice ] += 1\n", " bb_score[ k ] = result \n", " self.N += 1\n", " choices[ k ] = choice\n", " \n", " self.bb_score = np.r_[ self.bb_score, bb_score ]\n", " self.choices = np.r_[ self.choices, choices ]\n", " return " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we visualize the learning of the Bayesian Bandit solution." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import scipy.stats as stats\n", "figsize( 11.0, 10)\n", "\n", "beta = stats.beta\n", "x = np.linspace(0.001,.999,200)\n", "\n", "def plot_priors(bayesian_strategy, prob, lw = 3, alpha = 0.2, plt_vlines = True):\n", " ## plotting function\n", " wins = bayesian_strategy.wins\n", " trials = bayesian_strategy.trials\n", " for i in range( prob.shape[0] ):\n", " y = beta( 1+wins[i], 1 + trials[i] - wins[i] )\n", " p = plt.plot( x, y.pdf(x), lw = lw )\n", " c = p[0].get_markeredgecolor()\n", " plt.fill_between(x,y.pdf(x),0, color = c, alpha = alpha, \n", " label=\"underlying probability: %.2f\"%prob[i])\n", " if plt_vlines:\n", " plt.vlines( prob[i], 0, y.pdf(prob[i]) ,\n", " colors = c, linestyles = \"--\", lw = 2 )\n", " plt.autoscale(tight = \"True\")\n", " plt.title(\"Posteriors After %d pull\"%bayesian_strategy.N +\\\n", " \"s\"*(bayesian_strategy.N>1) )\n", " plt.autoscale(tight=True)\n", " return" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "hidden_prob = np.array([0.85, 0.60, 0.75] )\n", "bandits = Bandits( hidden_prob )\n", "bayesian_strat = BayesianStrategy( bandits )\n", "\n", "draw_samples = [1, 1, 3, 10, 10, 25, 50, 100, 200, 600 ]\n", "\n", "for j,i in enumerate(draw_samples):\n", " subplot( 5, 2, j+1) \n", " bayesian_strat.sample_bandits(i)\n", " plot_priors( bayesian_strat, hidden_prob )\n", " #plt.legend()\n", " plt.autoscale( tight = True )\n", "plt.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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T965w6hEK5x6hkPcMpQnRpMVQA8JK5OQYr+gJlU9TUBmZZqvlU5t7Q9dgiE9E6dGT0NQq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zZh06ZN5nIZjUaIxWI8//zz2LJlCyIjI1FTU2P1XJ1Oh9bWVkRGRgIAIiMjcejQoUGv0djY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\n1Ae33JGKQ3tLoVHrodMa8Nk/C1GsqQGmhgMch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} ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we don't real care how accurate we become about inference of the hidden probabilities — for this problem we are more interested in choosing the best bandit (or more accurately, becoming *more confident* in choosing the best bandit). For this reason, the distribution of the red bandit is very wide (representing ignorance about what that hidden probability might be) but we are reasonably confident that it is not the best, so the algorithm chooses to ignore it.\n", "\n", "From the above, we can see that after 1000 pulls, the majority of the \"blue\" function leads the pack, hence we will almost always choose this arm. This is good, as this arm is indeed the best.\n", "\n", "Below is a D3 app that demonstrates our algorithm updating/learning three bandits. The first figure are the raw counts of pulls and wins, and the second figure is a dynamically updating plot. I encourage you to try to guess which bandit is optimal, prior to revealing the true probabilities, by selecting the `arm buttons`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.core.display import HTML\n", "\n", "#try executing the below command twice if the first time doesn't work\n", "HTML(filename = \"BanditsD3.html\" )" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " \n", " \n", "\n", " \n", "\n", "\n", " \n", "
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Rewards

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Pulls

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Reward/Pull Ratio

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\n", "\n", "\n" ], "output_type": "pyout", "prompt_number": 4, "text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deviations of the observed ratio from the highest probability is a measure of performance. For example,in the long run, optimally we can attain the reward/pull ratio of the maximum bandit probability. Long-term realized ratios less than the maximum represent inefficiencies. (Realized ratios larger than the maximum probability is due to randomness, and will eventually fall below). \n", "\n", "### A Measure of *Good*\n", "\n", "We need a metric to calculate how well we are doing. Recall the absolute *best* we can do is to always pick the bandit with the largest probability of winning. Denote this best bandit's probability of $w_{opt}$. Our score should be relative to how well we would have done had we chosen the best bandit from the beginning. This motivates the *total regret* of a strategy, defined:\n", "\n", "\\begin{align}\n", "R_T & = \\sum_{i=1}^{T} \\left( w_{opt} - w_{B(i)} \\right)\\\\\\\\\n", "& = Tw^* - \\sum_{i=1}^{T} \\; w_{B(i)} \n", "\\end{align}\n", "\n", "\n", "where $w_{B(i)}$ is the probability of a prize of the chosen bandit in the $i$ round. A total regret of 0 means the strategy is matching the best possible score. This is likely not possible, as initially our algorithm will often make the wrong choice. Ideally, a strategy's total regret should flatten as it learns the best bandit. (Mathematically we achieve $w_{B(i)}=w_{opt}$ often)\n", "\n", "\n", "Below we plot the total regret of this simulation, including the scores of some other strategies:\n", "\n", "1. Random: randomly choose a bandit to pull. If you can't beat this, just stop. \n", "2. largest Bayesian credible bound: pick the bandit with the largest upper bound in its 95% credible region of the underlying probability. \n", "3. Bayes-UCB algorithm: pick the bandit with the largest *score*, where score is a dynamic quantile of the posterior (see [4] )\n", "3. Mean of posterior: choose the bandit with the largest posterior mean. This is what a human player (sans computer) would likely do. \n", "3. Largest proportion: pick the bandit with the current largest observed proportion of winning. \n", "\n", "The code for these are in the `other_strats.py`, where you can implement your own very easily." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.5, 5 )\n", "\n", "from other_strats import *\n", "\n", "#define a harder problem\n", "hidden_prob = np.array([0.15, 0.2, 0.1, 0.05] )\n", "bandits = Bandits( hidden_prob )\n", "\n", "\n", "#define regret\n", "def regret( probabilities, choices ):\n", " w_opt = probabilities.max()\n", " return ( w_opt - probabilities[choices.astype(int)] ).cumsum()\n", "\n", "\n", "#create new strategies\n", "\n", "strategies= [upper_credible_choice, \n", " bayesian_bandit_choice, \n", " ucb_bayes , \n", " max_mean,\n", " random_choice ]\n", "algos = []\n", "for strat in strategies:\n", " algos.append( GeneralBanditStrat( bandits, strat ))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "#train 10000 times\n", "for strat in algos:\n", " strat.sample_bandits( 10000)\n", " \n", "#test and plot\n", "for i,strat in enumerate(algos):\n", " _regret = regret( hidden_prob, strat.choices )\n", " plt.plot( _regret, label = strategies[i].__name__, lw = 3)\n", "\n", "plt.title(\"Total Regret of Bayesian Bandits Strategy vs. Random guessing\" )\n", "plt.xlabel(\"Number of pulls\")\n", "plt.ylabel(\"Regret after $n$ pulls\");\n", "plt.legend(loc = \"upper left\");" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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f5OTkwNTUFMDT8aafvUTj9u3bciMLWFpayg37xRhjjDHGGKsZlbxQLCUlBcuW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IAAAg\nAElEQVT7V0GFxSFG1+F+GiQ9R2BMz9u+ni/mZkrjXzvJPF7hCqkXUVNSK8LXZCAgfEpRFGwFhzBn\nrcS8Ox17yVnHIJUafdfRNEh6loCWHbyf5G2Qxl8IIYQQ/krWCAifUGxWzHuWU7pxPpXnjzmN0Ya1\nw5AwHkO3MWgatvByhrdGGn8hhBBCeIKsERC1nt1ahmn7Eso2LcB+pcDhvDokFEOPZPRxwwiI7un3\ni3+l8RdCCCFEbSUDAeEVtvMnMG3/R9X0n9IL151T6YLRdRiEoetodLFDUGm8U5a3MjdTGv/6Sebx\nCldIvYiakloRviYDAeExSrmJ8lO7Me1aiiXrS1Ds151XBzcnqN+TGO95HLU+xEdZ3pw0/kIIIYSo\nq3y2RmDSpEl8/fXXNG/enIMHDwJQXFxMSkoKubm5REdHs3z5cho1agTA3LlzWbx4MRqNhvfff5/B\ngwc7vKesEfA9RVGoOLkL875VmLNWoJQVO8SoG4XTIOk5jAmpqAL0PsjyxqTxF0IIIYQ/qlNrBB5/\n/HGeeeYZHnvsserX0tLSGDRoEC+88ALz5s0jLS2NtLQ0srOzWbZsGdnZ2eTn55OUlEROTg5qtdpX\n6YvfqLx6Dsu+rzBlfo7tzAGnMYFt+xN07x/QtRvgtek/v0cafyGEEELUVz7rxvr27cupU6eue23N\nmjVs3rwZgIkTJ9KvXz/S0tJYvXo148aNIyAggOjoaFq3bk1mZiaJiYk+yFxco9jtWA9vwLTzU6y/\n/AB2m0OMumEL9B2GYEh8lMAo339b8+vGP2PTRmhy9abx0vgLkHm8wjVSL6KmpFaEr/nHbdl/OXv2\nLKGhoQCEhoZy9mzVnvIFBQXXNf0RERHk5+f7JMf6TlEUKk7sxLzvKyyHvsF+2XHnH7Q6DN3HYug2\nhsDW96DSBHg/0X+52R3/4lIzTZoYrouXxl8IIYQQ9YVfDQR+TaVS3XTryBudmz59OlFRUQCEhIQQ\nFxdXPdreunUrgBzfwrHtwkkylrxF+dGf6K6vav4ziwAgPqzqf7Noi67dAAY89p+ojY2q/v75XV7N\nt8R0iZAIbfUd/+LSczSJqmr2i/PMANXHACX5lfTqlUhsVHcsRVrC74ih3339qt/vYm6mX/z7y7Fv\nj/v06eNX+cixfx9LvcixHMuxO44Btm3bRl5eHgCTJ0/G3Xz6QLFTp04xfPjw6sXC7dq1Y9OmTYSF\nhVFYWEj//v05cuQIaWlpALz44osA3H///bz++uskJCRc936yWNh9FEWhIi8Ly89rsRxYR+WFE07j\nVMbGGBMnYOw1AW2zVl7OUub4CyGEEKJ+qFOLhZ0ZMWIES5YsYfbs2SxZsoRRo0ZVv56amsrMmTPJ\nz8/n6NGjxMfH+zjbuqny6vmq/f73rqDy3FGnMSpdA/TdxmDo9hCBdyV6deqPOxv/rVu30j5SBgHi\n923dKvN4Rc1JvYiakloRvuazgcC4cePYvHkzFy5cIDIykj/+8Y+8+OKLJCcns2jRourtQwFiY2NJ\nTk4mNjYWrVbLggUL/P6Js7VJ5dXzWI9sxHr4OyyH1oPN6hikCUDXtj+GhFT07QehCjQ4xniA3PEX\nQgghhPAMn04NcjeZGlRzSrkJ65EMyrb9g/KcH8FJGagCg9B3ehB919Ho2t6HSqvzeF7S+AshhBBC\nOKrzU4OEZymKQvnxbZgz0zHv+woqzE7jAqK6EXTfE+jjHkAVaPRoTtL4CyGEEEL4hgwE6jhFUbDl\nH8RyaD3mvV9Sef6Y07iAmAT0HYagix2EtkWsx6Ze+VPjL3MzRU1JrQhXSL2ImpJaEb4mA4E6SFEU\nKnL3YDmwDsu+r6i8dMZpnDa0Lbq4BzAmTkDbNNojufhT4y+EEEIIIf5N1gjUEUqljYrcvVh/+QHL\nofXYCrOdxql0wRh6jMXQI4XAmJ5uz0MafyGEEEII95M1AsKBrfh01XafmUuxl5x1GqMyNEQXOxh9\nx/vRdxji1nn/0vgLIYQQQtROMhCohZQKC5bDGzDvWoo1ZzNUVjgGaXUYuj2EvvNwdG37o3JTs12X\nGn+ZmylqSmpFuELqRdSU1IrwNRkI1CK288cp27wQ855lKJarDufVIaHoYgeja5+E7u77UBtCbvua\ndanx///bu/PgqKp8gePfe29vSSchCyGBhBhMwo5EH7vjA52JM27ooIO44V6vtHR0xpminCoccUqF\n0akacabevFFQB2ZkHlJPfQ7yKFSePMEgE3BDZDGBLOwxmIX0ds/7ozud7vSS7hAISX6fErvvOeee\nc+7tk+7fuX37XiGEEEII0Ul+I3CeU0rhqa6kdfO/0/75O1Gv928dNR3nnAdwTLwazTizuZ0E/kII\nIYQQ5x/5jcAg4ms+zukd/0nbtr/gO7YvIt8YOoqUKfNJmboAS84FPW5HAn8hhBBCiMFJJgLnEeV1\n0/7Fetq2rcK9939BmRFl7OMrcM5+ANvo2T261r8E/p3k3EyRKBkrIhkyXkSiZKyIviYTgfOA2XKS\ntm2v0fp/KzBPHY7I1+zpOC75Mc5//Tesw8clVbcE/kIIIYQQIhr5jUAfUUrhPrCVtg//g/YvNoDp\nDS+gadhGzSBl2gIcF89DtzsTqlcCfyGEEEKIgUd+IzAA+JqP4fpyI63/twJv3acR+XpGHqkzFpIy\n4zYs2UXd1ieBvxBCCCGE6AmZCJwDSincX39A60crcX35P2D6IspYi6eSOusuUi6Zh2axx6xLAv/e\nI+dmikTJWBHJkPEiEiVjRfQ1mQicJUopPDU7aP/8H7Tv+i98jVECdquD1KkLSP3Xf8OaPyZqPRL4\nC9E/KVOhlMJU/vcD/7L/uWkq3C4vpulPDz4qhc9r4vWYwXId63o9Jl6vL1hHx0mdweeqs/7Q9GAe\nkf3A/18w379il7TA/zrb67qsQtI7+xGaZ5qRZ6AmdFJqlEJRV4uSqLomRi1zduras3c/jbVp0Tcy\nkaRE+pBwXWeyD6OV6/6Fi1bENBWmz+y2XLRWkzmBudfrPMv7b3/1FxzYGeXCH2cwBkxT4fWEH3BM\nZHu7O1O8N+qIWk8Px1SybScyNhJrJ34d0ZJ69HcZpdo583Lj9q0nZCLQi5SnHdfeD3FXV9L+2TtR\nL/sJ/qP/9nE/wHnpPehpOWF5EvifO3IURiQq3lhxtXv47JM6Pt1ey3dNp4OBthi8dPLZ+/mRvu6G\n6AcyHMUcPxx5g1AhzhWZCPQC7/FvaNv2Gqe3v47ZciJqGS1lCClT5uO87H4sw0qD6RL4Dy6q4xCt\n8h/pDRwu7jw6q8zOfFOFPTfbXZ3roLrUhf+5aXY+VwqFQpkmPm9He/585fXhO+0CupQPHlnu6I8K\nqwsTAhkhR6L9aZ39pbN8WDmF8vpC+h7cKZ3tBKuPkkZnPzvXC1k/uH8Jr5uQfgHK50P5TJQyUaYJ\nJsFllIkKLKMCR+VdbpTX17lPTH+dp4w0TtqyOGHLxqfLW6kQQoj+Rz69esjXcgLX5+s5vfNN3Hs3\nRy2j2VJxlN+A46JrsY+9As1i8wf+u9/t08BfmaY/8PH6UKYv6nOz3eVP8/kwvT7wmZg+rz/N68UX\nzDcDeT7oCLB8PjynWjDdbky3B+X24G1rR3m94UGfGRrMQmhwGxoEhwW6wYA0PJg2A3V3DWLduo3v\nHJl4dQOFjqkF/qHx9YmDlOZeiNI0vLoVj2FDaRoKDdD88WTHcuDRa7HhNaxdvrJTgXVi7G+loCM/\nrJgW5WlnWrCJmPeLiF+nCq1T12P279w6X/qRAC3wLwUONuzmghHjk6/DNNGC49j0jypToaHQ3S40\n04cWmPxppn/yoZkmutfjTwvJ00wfutftX4aQSZFCC/z9dKRpHTOnYH7n5EkL9qUjP+TRvxBSX+Cx\nY126pAceo9cV3i8trI3OtuItxkyMkqRFX7nLeol+VdN9m1HbCyTtbTvO6NTc8MRe6Fu8NrtNTOS8\ng2ht9uxciahldJ+3+3KJ1hdwRvvkDNpOaL/EajckaY+7ibG2zG7LBdtNcDt0j6vb1zzqJ0t325XQ\ndkeW0Xoy/nrQl8ht6sF7TAJlItrpyX5JpJ2uZW5ankA7yZGJQBLMlpOcrlrH6Z3/hafmE6Ld8EvP\nLMAx6Rrsoy/DPuZyGl3N7KitYvemZWcc+Cufj/bDxzl9qhnvqRa8zS14mr7jdO0RXMdO4ms7jeny\n4HO5MdtdtDccxdfWjunxorz+IN70ejFPu87K/kmWApRhoW1YIZ7UDJTFgmlYURYrPqsVZVgxLTa8\nKU6UYUFpuj8o1jRU6KOhga0zzWdz4HOkYhrWuAHwUa/CkTv63G2wGLDsTcfJ+eJjhnzzhT/YUfGm\nhuK8o+vhN2jseBqWpoU8jTaJ7yyT7m0hu7k5Ip0Y62kx2glvM7KdWHVrUQ8yxNuG+Nseq6xmGKBp\nnUmhfQk8D8vT9PD+BcsTUj60DqKk+dMtqakx92fc7Yu1vUmup0WsGKP+rut1yWs62cAFQ0dEXS9+\nX2K3F/76x+sLMfMilkOeGyl2dIulMz3k9Ql/vbu+poSXjTIOIl7rkG3VItqK/XegaRq6w95ZZ+Cf\npnWtO9APLaTOkLHXNc3fpkb49oXUGWhDMywRf0talz5GfQ+IUaZjX8WPIHtG7iOQAHf1dlo/+CPt\nX6yPesUfNA37+CtJnbmQlsKL2NPwWdJH/MfmTaLEcSEjPJmYJ1twHztJ+5HjuI6cwHX0BO1HT9Je\ndwTT5U6q7wpA01F6xz+j89GwoAwLpmHBtNowLVZ8thRMqw1lsQaWHSjDgs9qw7TaOkZ8MOj2B+P+\nAF0F9kVHgK4MKx5nBkrX/X0IC+L1KO9C4mzxH3mOOKQZWS5uLZ3fbCR6VCpqfbE/gxOvJ8m+axD1\nw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} ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Like we wanted, Bayesian bandits and other strategies have decreasing rates of regret, representing we are achieving optimal choices. To be more scientific so as to remove any possible luck in the above simulation, we should instead look at the *expected total regret*:\n", "\n", "$$\\bar{R_T} = E[ R_T ] $$\n", "\n", "It can be shown that any *sub-optimal* strategy's expected total regret is bounded below logarithmically. Formally,\n", "\n", "$$ E[R_T] = \\Omega \\left( \\;\\log(T)\\; \\right)$$\n", "\n", "Thus, any strategy that matches logarithmic-growing regret is said to \"solve\" the Multi-Armed Bandit problem [3].\n", "\n", "Using the Law of Large Numbers, we can approximate Bayesian Bandit's expected total regret by performing the same experiment many times (500 times, to be fair):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#this can be slow, so I recommend NOT running it. \n", "\n", "trials = 500\n", "expected_total_regret = np.zeros( ( 10000, 3 ) )\n", "\n", "for i_strat, strat in enumerate( strategies[:-2] ):\n", " for i in range(trials):\n", " general_strat = GeneralBanditStrat( bandits, strat )\n", " general_strat.sample_bandits(10000)\n", " _regret = regret( hidden_prob, general_strat.choices ) \n", " expected_total_regret[:,i_strat] += _regret\n", " \n", " plot(expected_total_regret[:,i_strat]/trials, lw =3, label = strat.__name__ )\n", " \n", "plt.title(\"Expected Total Regret of Multi-armed Bandit strategies\" )\n", "plt.xlabel(\"Number of pulls\")\n", "plt.ylabel(\"Exepected Total Regret \\n after $n$ pulls\");\n", "plt.legend(loc = \"upper left\");" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0\n", "1" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "2" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "output_type": "pyout", "prompt_number": 24, "text": [ "" ] }, { "output_type": "display_data", "png": 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Ro3Hp0iU899xzeOGFF/D888/XmZQAAHr16lXlvW+++QbffvstUlNToVarodfr6+zj0pBj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\njh1DcHAwysrKsGrVK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} ], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure()\n", "[pl1, pl2, pl3] = plt.plot( expected_total_regret[:, [0,1,2]], lw = 3 )\n", "plt.xscale(\"log\")\n", "plt.legend([ pl1, pl2, pl3], \n", " [\"Upper Credible Bound\", \"Bayesian Bandit\", \"UCB-Bayes\"],\n", " loc=\"upper left\")\n", "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");\n", "plt.title( \"log-scale of above\" );\n", "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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w119/8eKLL+Y6NldXV3bt2kVERASTJk1i1KhR3Lx5Uz0eGBiIp6cnV69e5d13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} ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Extending the algorithm \n", "\n", "\n", "Because of the Bayesian Bandits algorithm's simplicity, it is easy to extend. Some possibilities:\n", "\n", "- If interested in the *minimum* probability (eg: where prizes are are bad thing), simply choose $B = \\text{argmin} \\; X_b$ and proceed.\n", "\n", "- Adding learning rates: Suppose the underlying environment may change over time. Technically the standard Bayesian Bandit algorithm would self-update itself (awesome) by noting that what it thought was the best is starting to fail more often, we can motivate the algorithm to learn changing environments quicker. We simply need to add a *rate* term upon updating:\n", "\n", " self.wins[ choice ] = rate*self.wins[ choice ] + result\n", " self.trials[ choice ] = rate*self.trials[ choice ] + 1\n", "\n", " If `rate < 1`, the algorithm will *forget* its previous wins quicker and there will be a downward pressure towards ignorance. Conversely, setting `rate > 1` implies your algorithm will act more risky, and bet on earlier winners more often and be more resistant to changing environments. \n", "\n", "- Hierarchical algorithms: We can setup a Bayesian Bandit algorithm on top of smaller bandit algorithms. Suppose we have $N$ Bayesian Bandit models, each varying in some behavior (for example different `rate` parameters, representing varying sensitivity to changing environments). On top of these $N$ models is another Bayesian Bandit learner that will select a sub-Bayesian Bandit. This chosen Bayesian Bandit will then make an internal choice as to which machine to pull. The super-Bayesian Bandit updates itself depending on whether the sub-Bayesian Bandit was correct or not. \n", "\n", "- Extending the rewards, denoted $y_a$ for bandit $a$, to random variables from a distribution $f_{y_a}(y)$ is straightforward. More generally, this problem can be rephrased as \"Find the bandit with the largest expected value\", as playing the bandit with the largest expected value is optimal. In the case above, $f_{y_a}$ was Bernoulli with probability $p_a$, hence the expected value for an bandit is equal to $p_a$, which is why it looks like we are aiming to maximize the probability of winning. If $f$ is not Bernoulli, and it is non-negative, which can be accomplished apriori by shifting the distribution (we assume we know $f$), then the algorithm behaves as before:\n", "\n", " For each round, \n", " \n", " 1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", " 2. Select the bandit with largest sample, i.e. select bandit $B = \\text{argmax}\\;\\; X_b$.\n", " 3. Observe the result,$R \\sim f_{y_a}$, of pulling bandit $B$, and update your prior on bandit $B$.\n", " 4. Return to A\n", "\n", " The issue is in the sampling of $X_b$ drawing phase. With Beta priors and Bernoulli observations, we have a Beta posterior — this is easy to sample from. But now, with arbitrary distributions $f$, we have a non-trivial posterior. Sampling from these can be difficult.\n", "\n", "- There has been some interest in extending the Bayesian Bandit algorithm to commenting systems. Recall in Chapter 4, we developed a ranking algorithm based on the Bayesian lower-bound of the proportion of upvotes to total total votes. One problem with this approach is that it will bias the top rankings towards older comments, since older comments naturally have more votes (and hence the lower-bound is tighter to the true proportion). This creates a positive feedback cycle where older comments gain more votes, hence are displayed more often, hence gain more votes, etc. This pushes any new, potentially better comments, towards the bottom. J. Neufeld proposes a system to remedy this that uses a Bayesian Bandit solution.\n", "\n", "His proposal is to consider each comment as a Bandit, with a the number of pulls equal to the number of votes cast, and number of rewards as the number of upvotes, hence creating a $\\text{Beta}(1+U,1+D)$ posterior. As visitors visit the page, samples are drawn from each bandit/comment, but instead of displaying the comment with the $\\max$ sample, the comments are ranked according the the ranking of their respective samples. From J. Neufeld's blog [7]:\n", "\n", " > [The] resulting ranking algorithm is quite straightforward, each new time the comments page is loaded, the score for each comment is sampled from a $\\text{Beta}(1+U,1+D)$, comments are then ranked by this score in descending order... This randomization has a unique benefit in that even untouched comments $(U=1,D=0)$ have some chance of being seen even in threads with 5000+ comments (something that is not happening now), but, at the same time, the user will is not likely to be inundated with rating these new comments. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just for fun, though the colors explode, we watch the Bayesian Bandit algorithm learn 15 different options. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.0, 8)\n", "beta = stats.beta\n", "hidden_prob = beta.rvs(1,13, size = 35 )\n", "print hidden_prob\n", "bandits = Bandits( hidden_prob )\n", "bayesian_strat = BayesianStrategy( bandits )\n", "\n", "for j,i in enumerate([100, 200, 500, 1300 ]):\n", " subplot( 2, 2, j+1) \n", " bayesian_strat.sample_bandits(i)\n", " plot_priors( bayesian_strat, hidden_prob, lw = 2, alpha = 0.0, plt_vlines=False )\n", " #plt.legend()\n", " plt.xlim(0, 0.5 )\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 1.05872577e-02 2.44329406e-02 2.17921542e-01 2.84275845e-02\n", " 1.79636306e-01 1.76434301e-01 1.03803619e-01 3.41231782e-02\n", " 1.51276511e-01 2.02988173e-05 8.25837083e-02 3.00819469e-02\n", " 3.87676920e-02 9.95699292e-02 5.74074773e-02 8.88739680e-02\n", " 3.04542676e-02 7.08154796e-02 8.18108782e-03 1.45369509e-01\n", " 6.87009381e-03 8.52942080e-02 1.28626668e-02 7.84557611e-02\n", " 1.84449164e-01 6.52984488e-02 4.34863358e-02 4.39868639e-02\n", " 4.82796284e-02 7.85578667e-02 2.20346874e-01 4.95440403e-02\n", " 4.70066750e-02 8.37623221e-02 5.95142751e-02]\n" ] }, { "output_type": "display_data", "png": 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9+9KrVy8AnnzyyXrt8mw1+FzM5NX/rGjwPBGutUs/d78QQ0pGMlD7wt2l6dlO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\nXZS6eEefvoGkHDxJkpkdRc4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GX/f2Rl0+VpJak6KiIvbv389nn30G1A6D+HtB3BjL37if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5z9+2r45I1NfGzZTXGAhUBBz6LLZ/PsDf3JvC+d+0fEIArwyY4qtpj7Y4y/G4D80Fb0v9xF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\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fHaR4cg9KcoRgvpGb115DU+HpSyHRZ/8JebaHXu21eKzN9GQFrr59Gfo36Yj+qWcHewMT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\nYuJCEXGxiLhQSO9shLry1Rg1eszigkb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} ], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Eliciting expert prior\n", "\n", "Specifying a subjective prior is how practitioners incorporate domain knowledge about the problem into our mathematical framework. Allowing domain knowledge is useful for many reasons:\n", "\n", "- Aids speeds of MCMC convergence. For example, if we know the unknown parameter is strictly positive, then we can restrict our attention there, hence saving time that would otherwise be spent exploring negative values.\n", "- More accurate inference. By weighing prior values near the true unknown value higher, we are narrowing our eventual inference (by making the posterior tighter around the unknown) \n", "- Express our uncertainty better. See the *Price is Right* problem in Chapter 3.\n", "\n", "plus many other reasons. Of course, practitioners of Bayesian methods are not experts in every field, so we must turn to domain experts to craft our priors. We must be careful with how we elicit these priors though. Some things to consider:\n", "\n", "1. From experience, I would avoid introducing Betas, Gammas, etc. to non-Bayesian practitioners. Furthermore, non-statisticians can get tripped up by how a continuous probability function can have a value exceeding one.\n", "\n", "2. Individuals often neglect the rare *tail-events* and put too much weight around the mean of distribution. \n", "\n", "3. Related to above is that almost always individuals will under-emphasize the uncertainty in their guesses.\n", "\n", "Eliciting priors from non-technical experts is especially difficult. Rather than introduce the notion of probability distributions, priors, etc. that may scare an expert, there is a much simpler solution. \n", "\n", "###Trial roulette method \n", "\n", "\n", "The *trial roulette method* [8] focuses on building a prior distribution by placing counters (think casino chips) on what the expert thinks are possible outcomes. The expert is given $N$ counters (say $N=20$) and is asked to place them on a pre-printed grid, with bins representing intervals. Each column would represent their belief of the probability of getting the corresponding bin result. Each chip would represent an $\\frac{1}{N} = 0.05$ increase in the probability of the outcome being in that interval. For example [9]:\n", "\n", "> A student is asked to predict the mark in a future exam. The figure below shows a completed grid for the elicitation of a subjective probability distribution. The horizontal axis of the grid shows the possible bins (or mark intervals) that the student was asked to consider. The numbers in top row record the number of chips per bin. The completed grid (using a total of 20 chips) shows that the student believes there is a 30% chance that the mark will be between 60 and 64.9.\n", "\n", "\n", "\n", "\n", "From this, we can fit a distribution that captures the expert's choice. Some reasons in favor of using this technique are:\n", "\n", "1. Many questions about the shape of the expert's subjective probability distribution can be answered without the need to pose a long series of questions to the expert - the statistician can simply read off density above or below any given point, or that between any two points.\n", "\n", "2. During the elicitation process, the experts can move around the chips if unsatisfied with the way they placed them initially - thus they can be sure of the final result to be submitted.\n", "\n", "3. It forces the expert to be coherent in the set of probabilities that are provided. If all the chips are used, the probabilities must sum to one.\n", "\n", "4. Graphical methods seem to provide more accurate results, especially for participants with modest levels of statistical sophistication." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Example: Stock Returns\n", "\n", "\n", "Take note stock brokers: you're doing it wrong. When choosing which stocks to pick, an analyst will often look at the *daily return* of the stock. Suppose $S_t$ is the price of the stock on day $t$, then the daily return on day $t$ is :\n", "\n", "$$r_t = \\frac{ S_t - S_{t-1} }{ S_{t-1} } $$\n", "\n", "The *expected daily return* of a stock is denoted $\\mu = E[ r_t ] $. Obviously, stocks with high expected returns are desirable. Unfortunately, stock returns are so filled with noise that it is very hard to estimate this parameter. Furthermore, the parameter might change over time (consider the rises and falls of AAPL stock), hence it is unwise to use a large historical dataset. \n", "\n", "Historically, the expected return has been estimated by using the sample mean. This is a bad idea. As mentioned, the sample mean of a small dataset size has enormous potential to be very wrong (again, see Chapter 4 for full details). Thus Bayesian inference is the correct procedure here, since we are able to see our uncertainty along with probable values.\n", "\n", "For this exercise, we will be examining the daily returns of the AAPL, GOOG, MSFT and AMZN. Before we pull in the data, suppose we ask our a stock fund manager (an expert in finance, but see [10] ), \n", "\n", "> What do you think the return profile looks like for each of these companies?\n", "\n", "Our stock broker, without needing to know the language of Normal distributions, or priors, or variances, etc. creates four distributions using the trial roulette method above. Suppose they look enough like Normals, so we fit Normals to them. They may look like: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import scipy.stats as stats\n", "figsize(11., 5 )\n", "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", "\n", "normal = stats.norm\n", "x = np.linspace( -0.15, 0.15, 100 )\n", "\n", "expert_prior_params = {\"AAPL\":(0.05, 0.03),\n", " \"GOOG\":(-0.03, 0.04 ), \n", " \"TSLA\": (-0.02, 0.01), \n", " \"AMZN\": (0.03, 0.02 ), \n", " }\n", "\n", "for i, (name, params) in enumerate(expert_prior_params.iteritems() ):\n", " subplot(2,2,i)\n", " y = normal.pdf( x, params[0], scale = params[1] )\n", " #plt.plot( x, y, c = colors[i] )\n", " plt.fill_between(x, 0, y, color = colors[i], linewidth=2,\n", " edgecolor = colors[i], alpha = 0.6)\n", " plt.title(name + \" prior\" )\n", " plt.vlines(0, 0, y.max(), \"k\",\"--\", linewidth = 0.5 )\n", " plt.xlim(-0.15, 0.15 )\n", "plt.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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/1uzsbNjt9v73c3JyYLPZBn2Otb6uLPaNYy1nscdA2D6pRfv2N8DrDcgsn5uw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\nG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} ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that these are subjective priors: the expert has a personal opinion on the stock returns of each of these companies, and is expressing them in a distribution. He's not wishful thinking -- he's introducing domain knowledge.\n", "\n", "In order to better model these returns, we should investigate the *covariance matrix* of the returns. For example, it would be unwise to invest in two stocks that are highly correlated, since they are likely to tank together (hence why fund managers suggest a diversification strategy). We will use the *Wishart distribution* for this, introduced earlier." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pymc as mc\n", "\n", "n_observations = 100 #we will truncate the the most recent 100 days.\n", "\n", "prior_mu = np.array( [ x[0] for x in expert_prior_params.values() ] )\n", "prior_std = np.array( [ x[1] for x in expert_prior_params.values() ] )\n", "\n", "inv_cov_matrix = mc.Wishart( \"inv_cov_matrix\", n_observations, diag(prior_std**2) )\n", "mu = mc.Normal( \"returns\", prior_mu, 1, size = 4 )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we pull historical data for these stocks:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# I wish I could have used Pandas as a prereq for this book, but oh well.\n", "\n", "import datetime\n", "import ystockquote as ysq\n", "\n", "stocks = [\"AAPL\", \"GOOG\", \"TSLA\", \"AMZN\" ]\n", "\n", "enddate = datetime.datetime.now().strftime(\"%Y-%m-%d\") #today's date.\n", "startdate = \"2012-09-01\"\n", "\n", "stock_closes = {}\n", "stock_returns = {}\n", "CLOSE = 6\n", "\n", "for stock in stocks:\n", " x = np.array( ysq.get_historical_prices( stock, startdate, enddate ) )\n", " stock_closes[stock] = x[1:,CLOSE].astype(float)\n", "\n", "#create returns:\n", "\n", "for stock in stocks:\n", " _previous_day = np.roll(stock_closes[stock],-1)\n", " stock_returns[stock] = ((stock_closes[stock] - _previous_day)/_previous_day)[:n_observations]\n", "\n", "dates = map( lambda x: datetime.datetime.strptime(x, \"%Y-%m-%d\" ), x[1:n_observations+1,0] ) " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 69 }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12.5, 4)\n", "\n", "for _stock, _returns in stock_returns.iteritems():\n", " p = plot( (1+_returns)[::-1].cumprod()-1, '-o', label = \"%s\"%_stock, \n", " markersize=4, markeredgecolor=\"none\" )\n", "\n", "plt.xticks( arange(100)[::-8], \n", " map(lambda x: datetime.datetime.strftime(x, \"%Y-%m-%d\"), dates[::8] ),\n", " rotation=60);\n", "\n", "plt.legend(loc = \"upper left\")\n", "plt.title(\"Return space\")\n", "plt.ylabel(\"Return of $1 on first date, x100%\");" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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cG7XyDWDVhJ2smrDTqLPwlIdiDfhdXV05duwYbdu2Be5cfQ4LC+OHH34waXGm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PMLkXnyYrn9pNz4GbkcVh7uMLO1Qd6N20KsZnWs0ezT0Wj8/juQK80Njqs20edncWoGss5fw6V/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\nh0sysQC2i2KFQoH16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} ], "prompt_number": 100 }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(11., 5 )\n", "returns = np.zeros( (n_observations,4 ))\n", "\n", "for i, (_stock,_returns) in enumerate(stock_returns.iteritems() ):\n", " \n", " returns[:,i] = _returns\n", " \n", " subplot(2,2,i)\n", " plt.hist( _returns, bins = 20, \n", " normed = True, histtype=\"stepfilled\",\n", " color = colors[i], alpha = 0.7 )\n", " plt.title(_stock + \" returns\" )\n", " plt.xlim(-0.15, 0.15 )\n", "\n", "plt.tight_layout()\n", "plt.suptitle(\"Histogram of daily returns\", size =14);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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4VqxYAQcHB633FEWBouMRvJwfx2VzLX/znx9QdPceOgZ3BgAkJh8BAHQM7gz3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\nSOLcOImZuQbC+iRmJv1IbE/SMnMNhAwSM6vhAIKIiIiIiCL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} ], "prompt_number": 121 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we perform the inference on the posterior mean return and posterior covariance matrix. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "obs = mc.MvNormal( \"observed returns\", mu, inv_cov_matrix, observed = True, value = returns )\n", "\n", "model = mc.Model( [obs, mu, inv_cov_matrix] )\n", "mcmc = mc.MCMC()\n", "\n", "mcmc.sample( 150000, 100000, 3 )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 120000 of 120000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 104 }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12.5,4)\n", "\n", "#examine the mean return first.\n", "mu_samples = mcmc.trace(\"returns\")[:]\n", "\n", "for i in range(4):\n", " plt.hist(mu_samples[:,i], alpha = 0.8 - 0.05*i, bins = 30,\n", " histtype=\"stepfilled\", normed=True, \n", " label = \"%s\"%stock_returns.keys()[i])\n", "\n", "plt.vlines( mu_samples.mean(axis=0), 0, 500, linestyle=\"--\", linewidth = .5 )\n", "\n", "plt.title(\"Posterior distribution of $\\mu$, daily stock returns\" )\n", "plt.legend();" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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4MFpaWozrVqxYgbCwMOzZs8dk3//zf/4PwsLCkJWVBQCYMGECBg4caPLp27cv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\nWidEREQkXWysk9043k56nDkTjKAX0FJV0/H2AAV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} ], "prompt_number": 122 }, { "cell_type": "markdown", "metadata": {}, "source": [ "(plots like these are what inspired the book's cover btw)\n", "\n", "What can we say about the results above? Clearly TSLA has been a strong performer, and our analysis suggests that it has an almost 1% daily return! Similarly, most of the distribution of AAPL is negative, suggesting that it's *true daily return* is negative.\n", "\n", "\n", "You may not have immediately noticed, but these variables are a whole order of magnitude *less* than our priors on them. For example, to put these one the same scale as the above prior distributions:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(11.0,3)\n", "for i in range(4):\n", " subplot(2,2,i+1)\n", " plt.hist(mu_samples[:,i], alpha = 0.8 - 0.05*i, bins = 30,\n", " histtype=\"stepfilled\", normed=True, color = colors[i],\n", " label = \"%s\"%stock_returns.keys()[i])\n", " plt.title( \"%s\"%stock_returns.keys()[i] )\n", " plt.xlim(-0.15, 0.15 )\n", " \n", "plt.suptitle(\"Posterior distribution of daily stock returns\" )\n", "plt.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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B6gZRXckYCGGvSjUGYsGCBSQkJHDhwgXWrVvHgAEDWL16NcOHDycqKgqAqKgo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\nRo8ezZAhQzhx4oTZMXP3U6luUO3+knhNyRiI6ku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} ], "prompt_number": 114 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Why did this occur? Recall how I mentioned that finance has a very very low signal to noise ratio. This implies an environment where inference is much more difficult. One should be careful about over interpreting these results: notice (in the first figure) that each distribution is positive at 0, implying that the stock may return nothing. Furthermore, the subjective priors influenced the results. From the fund managers point of view, this is good as it reflects his updated beliefs about the stocks, whereas from a neutral viewpoint this can be too subjective of a result. \n", "\n", "Below we show the posterior correlation matrix, and posterior standard deviations. An important caveat to know is that the Wishart distribution models the *inverse covariance matrix*, so we must invert it to get the covariance matrix. We also normalize the matrix to acquire the *correlation matrix*. Since we cannot plot hundreds of matrices effectively, we settle my summarizing the posterior distribution of correlation matrices of showing the *mean posterior correlation matrix* (defined on line 2)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "inv_cov_samples = mcmc.trace(\"inv_cov_matrix\")[:]\n", "mean_covariance_matrix = np.linalg.inv( inv_cov_samples.mean(axis=0) )\n", "\n", "\n", "def cov2corr( A ):\n", " \"\"\"\n", " covariance matrix to correlation matrix.\n", " \"\"\"\n", " d = np.sqrt(A.diagonal())\n", " A = ((A.T/d).T)/d\n", " #A[ np.diag_indices(A.shape[0]) ] = np.ones( A.shape[0] )\n", " return A\n", "\n", "\n", "subplot(1,2,1)\n", "plt.imshow( cov2corr(mean_covariance_matrix) , interpolation=\"none\", \n", " cmap = plt.cm.hot ) \n", "plt.xticks( arange(4), stock_returns.keys() )\n", "plt.yticks( arange(4), stock_returns.keys() )\n", "plt.colorbar(orientation=\"vertical\")\n", "plt.title(\"(mean posterior) Correlation Matrix\" )\n", "\n", "subplot(1,2,2)\n", "plt.bar(np.arange(4), np.sqrt(np.diag(mean_covariance_matrix)),\n", " color = \"#348ABD\", alpha = 0.7 )\n", "plt.xticks( np.arange(4) + 0.5, stock_returns.keys() );\n", "plt.title(\"(mean posterior) variances of daily stock returns\" )\n", "\n", "plt.tight_layout();\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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++SpSUlJS51eQapcpLS2Fg4MDDh06hF27dsHV1VV4FrDq5xJVl/wB4NKlS7Cz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\niTcxae0maGWhnsRTsW+fKPVoGlE1pLGusrIyODk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} ], "prompt_number": 118 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the above figures, we can say that likely TSLA has an above-average volatility (looking at the return graph this is quite clear). The correlation matrix shows that there are not strong correlations present, but perhaps GOOG and AMZN express a higher correlation (about 0.30). \n", "\n", "With this Bayesian analysis of the stock market, we can throw it into a Mean-Variance optimizer (which I cannot stress enough, do not use with frequentist point estimates) and find the minimum. This optimizer balances the tradeoff between a high return and high variance.\n", "\n", "$$ w_{opt} = \\min_{w} \\frac{1}{N}\\left( \\sum_{i=0}^N \\mu_i^T w - \\frac{\\lambda}{2}w^T\\Sigma_i w \\right)$$\n", "\n", "where $\\mu_i$ and $\\Sigma_i$ are the $i$th posterior estimate of the mean returns and the covariance matrix. This is another example of loss function optimization." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Protips for the Wishart distribution\n", "\n", "If you plan to be using the Wishart distribution, read on. Else, feel free to skip this. \n", "\n", "In the problem above, the Wishart distribution behaves pretty nicely. Unfortunately, this is rarely the case. The problem is that estimating an $NxN$ covariance matrix involves estimating $\\frac{1}{2}N(N-1)$ unknowns. This is a large number even for modest $N$. Personally, I've tried performing a similar simulation as above with $N = 23$ stocks, and ended up giving considering that I was requesting my MCMC simulation to estimate at least $\\frac{1}{2}23*22 = 253$ additional unknowns (plus the other interesting unknowns in the problem). This is not easy for MCMC. Essentially, you are asking you MCMC to traverse 250+ dimensional space. And the problem seemed so innocent initially! Below are some tips, in order of supremacy:\n", "\n", "1. Use conjugancy if it applies. See section below.\n", "\n", "2. Use a good starting value. What might be a good starting value? Why, the data's sample covariance matrix is! Note that this is not empirical Bayes: we are not touching the prior's parameters, we are modifying the starting value of the MCMC. Due to numerical instability, it is best to truncate the floats in the sample covariance matrix down a few degrees of precision (e.g. instability can cause unsymmetrical matrices, which can cause PyMC to cry.). \n", "\n", "3. Provide as much domain knowledge in the form of priors, if possible. I stress *if possible*. It is likely impossible to have an estimate about each $\\frac{1}{2}N(N-1)$ unknown. In this case, see number 4.\n", "\n", "4. Use empirical Bayes, i.e. use the sample covariance matrix as the prior's parameter.\n", "\n", "5. For problems where $N$ is very large, nothing is going to help. Instead, ask, do I really care about *every* correlation? Probably not. Further ask yourself, do I really really care about correlations? Possibly not. In finance, we can set an informal hierarchy of what we might be interested in the most: first a good estimate of $\\mu$, the variances along the diagonal of the covariance matrix are secondly important, and finally the correlations are least important. So, it might be better to ignore the $\\frac{1}{2}(N-1)(N-2)$ correlations and instead focus on the more important unknowns.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conjugate Priors\n", "\n", "Recall that a $\\text{Beta}$ prior with $\\text{Binomial}$ data implies a $\\text{Beta}$ posterior. Graphically:\n", "\n", "$$ \\underbrace{\\text{Beta}}_{\\text{prior}} \\cdot \\overbrace{\\text{Binomial}}^{\\text{data}} = \\overbrace{\\text{Beta}}^{\\text{posterior} } $$ \n", "\n", "Notice the $\\text{Beta}$ on both sides of this equation (no, you cannot cancel them, this is not a *real* equation). This is a really useful property. It allows us avoid using MCMC, since the posterior is known in closed form. Hence inference and analytics are easy to derive. This shortcut was the heart of the Bayesian Bandit algorithm above. Fortunately, there is an entire family of distributions that have similar behaviour. \n", "\n", "Suppose $X$ comes from, or is believed to come from, a well-known distribution, call it $f_{\\alpha}$, where $\\alpha$ are possibly unknown parameters of $f$. $f$ could be a Normal distribution, or Binomial distribution, etc. For particular distributions $f_{\\alpha}$, there may exist a prior distribution $p_{\\beta}$, such that:\n", "\n", "$$ \\overbrace{p_{\\beta}}^{\\text{prior}} \\cdot \\overbrace{f_{\\alpha}(X)}^{\\text{data}} = \\overbrace{p_{\\beta'}}^{\\text{posterior} } $$ \n", "\n", "where $\\beta'$ is a different set of parameters *but $p$ is the same distribution as the prior*. A prior $p$ that satisfies this relationship is called a *conjugate prior*. As I mentioned, they are useful computationally, as we can avoided approximate inference using MCMC and go directly to the posterior. This sounds great, right?\n", "\n", "Unfortunately, not quite. There are a few issues with conjugate priors.\n", "\n", "1. The conjugate prior is not objective. Hence only useful when a subjective prior is required. It is not guaranteed that the conjugate prior can accommodate the practitioner's subjective opinion.\n", "\n", "2. There typically exist conjugate priors for simple, one dimensional problems. For larger problems, involving more complicated structures, hope is lost to find a conjugate prior. For smaller models, Wikipedia has a nice [table of conjugate priors](http://en.wikipedia.org/wiki/Conjugate_prior#Table_of_conjugate_distributions).\n", "\n", "Really, conjugate priors are only useful for their mathematical convenience: it is simple to go from prior to posterior. I personally see conjugate priors as only a neat mathematical trick, and offer little insight into the problem at hand. \n", "\n", "## Jefferys Priors\n", "\n", "TODO." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Effect of the prior as $N$ increases\n", "\n", "In the first Chapter, I proposed that as the amount of observations, or data, that we posses, the less the prior matters. This is intuitive. After all, our prior is based on previous information, and eventually enough new information will shadow our previous information's value. The smothering of the prior by enough data is also helpful: if our prior is significantly wrong, then the self-correcting nature of the data will present to us a *less wrong*, and eventually *correct*, posterior. \n", "\n", "We can see this mathematically. First, recall Bayes Theorem from Chapter 1 that relates the prior to the posterior. The following is a sample from [What is the relationship between sample size and the influence of prior on posterior?](http://stats.stackexchange.com/questions/30387/what-is-the-relationship-between-sample-size-and-the-influence-of-prior-on-poste)[1] on CrossValidated.\n", "\n", ">The posterior distribution for a parameter $\\theta$, given a data set ${\\bf X}$ can be written as \n", "\n", "$$p(\\theta | {\\bf X}) \\propto \\underbrace{p({\\bf X} | \\theta)}_{{\\rm likelihood}} \\cdot \\overbrace{ p(\\theta) }^{ {\\rm prior} } $$\n", "\n", "\n", "\n", ">or, as is more commonly displayed on the log scale, \n", "\n", "$$ \\log( p(\\theta | {\\bf X}) ) = c + L(\\theta;{\\bf X}) + \\log(p(\\theta)) $$\n", "\n", ">The log-likelihood, $L(\\theta;{\\bf X}) = \\log \\left( p({\\bf X}|\\theta) \\right)$, **scales with the sample size**, since it is a function of the data, while the prior density does not. Therefore, as the sample size increases, the absolute value of $L(\\theta;{\\bf X})$ is getting larger while $\\log(p(\\theta))$ stays fixed (for a fixed value of $\\theta$), thus the sum $L(\\theta;{\\bf X}) + \\log(p(\\theta))$ becomes more heavily influenced by $L(\\theta;{\\bf X})$ as the sample size increases. \n", "\n", "There is an interesting consequence not immediately apparent. As the sample size increases, the chosen prior has less influence. Hence inference converges regardless of chosen prior, so long as the areas of non-zero probabilities are the same. \n", "\n", "Below we visualize this. We examine the convergence of two posteriors of a Binomial's parameter $\\theta$, one with a flat prior and the other with a biased prior towards 0. As the sample size increases, the posteriors, and hence the inference, converge." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize( 12.5, 15)\n", "\n", "p = 0.6\n", "beta1_params = np.array( [1.,1.] )\n", "beta2_params = np.array( [2,10] )\n", "beta = stats.beta\n", "\n", "x = np.linspace(0.00, 1, 125)\n", "data = mc.rbernoulli(p, size=500)\n", "\n", "figure()\n", "for i,N in enumerate([0,4,8, 32,64, 128, 500]):\n", " s = data[:N].sum() \n", " subplot(8,1,i+1)\n", " params1 = beta1_params + np.array( [s, N-s] )\n", " params2 = beta2_params + np.array( [s, N-s] )\n", " y1,y2 = beta.pdf( x, *params1), beta.pdf( x, *params2)\n", " plt.plot( x,y1, label = r\"flat prior\", lw =3 )\n", " plt.plot( x, y2, label = \"biased prior\", lw= 3 )\n", " plt.fill_between( x, 0, y1, color =\"#348ABD\", alpha = 0.15) \n", " plt.fill_between( x, 0, y2, color =\"#A60628\", alpha = 0.15) \n", " plt.legend(title = \"N=%d\"%N)\n", " plt.vlines( p, 0.0, 7.5, linestyles = \"--\", linewidth=1)\n", " #plt.ylim( 0, 10)#\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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EEA0REBBASUmJaRZFKcAdj8FgQKVSERwcbPVjW1R8q9VqVqxYQe/evSkpKaFf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r9Xprvu8L/fDDDzz88MMA9OrVi/z8fDIzG0/uVVF/bBkvvXv3xtPTE7CMl7S0tIboqmhgtowV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\nPCsr67LHfX1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ht/rNqsp7h0usm+m0cdXQz7/xTDe5mM+4u9F6exKjccGYmc3ZD7+wa/2X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\nM2jQICIjI0lISGDTpk1qX1paGvfccw9du3YlKiqqUQWQM2fOMHX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} ], "prompt_number": 138 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Keep in mind, not all posteriors will \"forget\" the prior this quickly. This example was just to show that *eventually* the prior is forgotten. The \"forgetfulness\" of the prior as we become awash in more and more data is the reason why Bayesian and Frequentist inference eventually converge as well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayesian perspective of Penalized Linear Regressions\n", "\n", "There is a very interesting relationship between a penalized least-squares regression and Bayesian priors. A penalized linear regression is a optimization problem of the form:\n", "\n", "$$ \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + f(\\beta)$$\n", "\n", "for some function $f$ (typically a norm like $|| \\cdot ||_p^p$). \n", "\n", "We will first describe the probabilistic interpretation of least-squares linear regression. Denote our response variable $Y$, and features are contained in the data matrix $X$. The standard linear model is:\n", "\n", "\\begin{equation}\n", "Y = X\\beta + \\epsilon\n", "\\end{equation}\n", "\n", "where $\\epsilon \\sim \\text{Normal}( {\\bf 0}, \\sigma{\\bf I })$. Simply, the observed $Y$ is a linear function of $X$ (with coefficients $\\beta$) plus some noise term. Our unknown to be determined is $\\beta$. We use the following property of Normal random variables:\n", "\n", "$$ \\mu' + \\text{Normal}( \\mu, \\sigma ) \\sim \\text{Normal}( \\mu' + \\mu , \\sigma ) $$\n", "\n", "to rewrite the above linear model as:\n", "\n", "\\begin{align}\n", "& Y = X\\beta + \\text{Normal}( {\\bf 0}, \\sigma{\\bf I }) \\\\\\\\\n", "& Y = \\text{Normal}( X\\beta , \\sigma{\\bf I }) \\\\\\\\\n", "\\end{align}\n", "\n", "In probabilistic notation, denote $f_Y(y \\; | \\; \\beta )$ the probability distribution of $Y$, and recalling the density function for a Normal random variable (see [here](http://en.wikipedia.org/wiki/Normal_distribution) ):\n", "\n", "$$ f_Y( Y \\; |\\; \\beta, X) = L(\\beta|\\; X,Y)= \\frac{1}{\\sqrt{ 2\\pi\\sigma} } \\exp \\left( \\frac{1}{2\\sigma^2} (Y - X\\beta)^T(Y - X\\beta) \\right) $$\n", "\n", "This is the likelihood function for $\\beta$. Taking the $\\log$:\n", "\n", "$$ \\ell(\\beta) = K - c(Y - X\\beta)^T(Y - X\\beta) $$\n", "\n", "where $K$ and $c>0$ are constants. Maximum likelihood techniques wish to maximize this for $\\beta$, \n", "\n", "$$\\hat{ \\beta } = \\text{argmax}_{\\beta} \\;\\; - (Y - X\\beta)^T(Y - X\\beta) $$\n", "\n", "Equivalently we can *minimize the negative* of the above:\n", "\n", "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) $$\n", "\n", "This is the familiar least-squares linear regression equation. Therefore we showed that the solution to a linear least-squares is the same as the maximum likelihood assuming Normal noise. Next we extend this to show how we can arrive at penalized linear regression by a suitable choice of prior on $\\beta$. \n", "\n", "#### Penalized least-squares\n", "\n", "In the above, once we have the likelihood, we can include a prior distribution on $\\beta$ to derive to the equation for the posterior distribution:\n", "\n", "$$P( \\beta | Y, X ) = L(\\beta|\\;X,Y)p( \\beta )$$\n", "\n", "where $p(\\beta)$ is a prior on the elements of $\\beta$. What are some interesting priors? \n", "\n", "1\\. If we include *no explicit* prior term, we are actually including an uninformative prior, $P( \\beta ) \\propto 1$, think of it as uniform over all numbers. \n", "\n", "2\\. If we have reason to believe the elements of $\\beta$ are not too large, we can suppose that *a priori*:\n", "\n", "$$ \\beta \\sim \\text{Normal}({\\bf 0 }, \\lambda {\\bf I } ) $$\n", "\n", "The resulting posterior density function for $\\beta$ is *proportional to*:\n", "\n", "$$ \\exp \\left( \\frac{1}{2\\sigma^2} (Y - X\\beta)^T(Y - X\\beta) \\right) \\exp \\left( \\frac{1}{2\\lambda^2} \\beta^T\\beta \\right) $$\n", "\n", "and taking the $\\log$ of this, and combining and redefining constants, we arrive at:\n", "\n", "$$ \\ell(\\beta) \\propto K - (Y - X\\beta)^T(Y - X\\beta) - \\alpha \\beta^T\\beta $$\n", "\n", "we arrive at the function we wish to maximize (recall the point that maximizes the posterior distribution is the MAP, or *maximum a posterior*):\n", "\n", "$$\\hat{ \\beta } = \\text{argmax}_{\\beta} \\;\\; -(Y - X\\beta)^T(Y - X\\beta) - \\alpha \\;\\beta^T\\beta $$\n", "\n", "Equivalently, we can minimize the negative of the above, and rewriting $\\beta^T \\beta = ||\\beta||_2^2$:\n", "\n", "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + \\alpha \\;||\\beta||_2^2$$\n", "\n", "This above term is exactly Ridge Regression. Thus we can see that ridge regression corresponds to the MAP of a linear model with Normal errors and a Normal prior on $\\beta$.\n", "\n", "3\\. Similarly, if we assume a *Laplace* prior on $\\beta$, ie. \n", "\n", "$$ f_\\beta( \\beta) \\propto \\exp \\left(- \\lambda ||\\beta||_1 \\right)$$\n", "\n", "and following the same steps as above, we recover:\n", "\n", "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + \\alpha \\;||\\beta||_1$$\n", "\n", "which is LASSO regression. Some important notes about this equivalence. The sparsity that is a result of using a LASSO regularization is not a result of the prior assigning high probability to sparsity. Quite the opposite actually. It is the combination of the $|| \\cdot ||_1$ function and using the MAP that creates sparsity on $\\beta$: [purely a geometric argument](http://camdp.com/blogs/least-squares-regression-l1-penalty). The prior does contribute to an overall shrinking of the coefficients towards 0 though. An interesting discussion of this can be found in [2].\n", "\n", "For an example of Bayesian linear regression, see Chapter 4's example on financial losses." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### References\n", "\n", "1. Macro, . \"What is the relationship between sample size and the influence of prior on posterior?.\" 13 Jun 2013. StackOverflow, Online Posting to Cross-Validated. Web. 25 Apr. 2013.\n", "\n", "2. Starck, J.-L., , et al. \"Sparsity and the Bayesian Perspective.\" Astronomy & Astrophysics. (2013): n. page. Print.\n", "\n", "3. Kuleshov, Volodymyr, and Doina Precup. \"Algorithms for the multi-armed bandit problem.\" Journal of Machine Learning Research. (2000): 1-49. Print.\n", "\n", "4. Gelman, Andrew. \"Prior distributions for variance parameters in hierarchical models.\" Bayesian Analysis. 1.3 (2006): 515-533. Print.\n", "\n", "5. Gelman, Andrew, and Cosma R. Shalizi. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 17 Apr. 2013.\n", "\n", "6. http://jmlr.csail.mit.edu/proceedings/papers/v22/kaufmann12/kaufmann12.pdf\n", "\n", "7. James, Neufeld. \"Reddit's \"best\" comment scoring algorithm as a multi-armed bandit task.\" Simple ML Hacks. Blogger, 09 Apr 2013. Web. 25 Apr. 2013.\n", "\n", "8. Oakley, J. E., Daneshkhah, A. and O\u2019Hagan, A. Nonparametric elicitation using the roulette method. Submitted to Bayesian Analysis.\n", "\n", "9. \"Eliciting priors from experts.\" 19 Jul 2010. StackOverflow, Online Posting to Cross-Validated. Web. 1 May. 2013. .\n", "\n", "10. Taleb, Nassim Nicholas (2007), The Black Swan: The Impact of the Highly Improbable, Random House, ISBN 978-1400063512" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"../styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "" ], "output_type": "pyout", "prompt_number": 1, "text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }